The starting price for the airport in the resort city, which is short-listed as a host city for the 2014 winter Olympics, was 3.5 billion rubles ($131.14 million) at the auction held by the Federal Property Fund.
Sochi has been bidding to host the 2014 Olympic Winter Games, along with Austria's Salzburg and South Korea's PyeongChang. The city bid for the 1998 and 2002 Winter Olympics, but was rejected largely due to its poor-quality Soviet-era infrastructure.
Russian television reported earlier in the day that the new owner will have to rebuild the airport, while the state has pledged to reconstruct the runways using money from the deal.
BasEl, owned by Oleg Dripaska, one of Russia's richest men who also controls Russian Aluminum (RusAl), holds combined assets of over $13 billion in energy, machinery, natural resources, financial services and construction.
A total of five companies took part in the auction, among them Renova, the asset management group controlled by Russian billionaire Viktor Vekselberg. Renova majority owns Sual [RTS: SUAL], Russia's second-largest aluminum producer, which recently merged with Deripaska's RusAl and Switzerland's Glencore to form the world's largest aluminum company.
Sochi International Airport received unwelcome publicity in May as the destination of an Armenian airliner that crashed into the Black Sea in stormy weather, killing all 113 passengers and crew on board.
Following a government order passed on July 3, 2006, the airport was included on a list of companies to be privatized in 2006. The airport has since been converted into a joint stock company with 100% state ownership.